Basics of Wavelets
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LNCS 7215, Pp
ACoreCalculusforProvenance Umut A. Acar1,AmalAhmed2,JamesCheney3,andRolyPerera1 1 Max Planck Institute for Software Systems umut,rolyp @mpi-sws.org { 2 Indiana} University [email protected] 3 University of Edinburgh [email protected] Abstract. Provenance is an increasing concern due to the revolution in sharing and processing scientific data on the Web and in other computer systems. It is proposed that many computer systems will need to become provenance-aware in order to provide satisfactory accountability, reproducibility,andtrustforscien- tific or other high-value data. To date, there is not a consensus concerning ap- propriate formal models or security properties for provenance. In previous work, we introduced a formal framework for provenance security and proposed formal definitions of properties called disclosure and obfuscation. This paper develops a core calculus for provenance in programming languages. Whereas previous models of provenance have focused on special-purpose languages such as workflows and database queries, we consider a higher-order, functional language with sums, products, and recursive types and functions. We explore the ramifications of using traces based on operational derivations for the purpose of comparing other forms of provenance. We design a rich class of prove- nance views over traces. Finally, we prove relationships among provenance views and develop some solutions to the disclosure and obfuscation problems. 1Introduction Provenance, or meta-information about the origin, history, or derivation of an object, is now recognized as a central challenge in establishing trust and providing security in computer systems, particularly on the Web. Essentially, provenance management in- volves instrumenting a system with detailed monitoring or logging of auditable records that help explain how results depend on inputs or other (sometimes untrustworthy) sources. -
11 Practice Lesso N 4 R O U N D W H Ole Nu M Bers U N It 1
CC04MM RPPSTG TEXT.indb 11 © Practice and Problem Solving Curriculum Associates, LLC Copying isnotpermitted. Practice Lesson 4 Round Whole Numbers Whole 4Round Lesson Practice Lesson 4 Round Whole Numbers Name: Solve. M 3 Round each number. Prerequisite: Round Three-Digit Numbers a. 689 rounded to the nearest ten is 690 . Study the example showing how to round a b. 68 rounded to the nearest hundred is 100 . three-digit number. Then solve problems 1–6. c. 945 rounded to the nearest ten is 950 . Example d. 945 rounded to the nearest hundred is 900 . Round 154 to the nearest ten. M 4 Rachel earned $164 babysitting last month. She earned $95 this month. Rachel rounded each 150 151 152 153 154 155 156 157 158 159 160 amount to the nearest $10 to estimate how much 154 is between 150 and 160. It is closer to 150. she earned. What is each amount rounded to the 154 rounded to the nearest ten is 150. nearest $10? Show your work. Round 154 to the nearest hundred. Student work will vary. Students might draw number lines, a hundreds chart, or explain in words. 100 110 120 130 140 150 160 170 180 190 200 Solution: ___________________________________$160 and $100 154 is between 100 and 200. It is closer to 200. C 5 Use the digits in the tiles to create a number that 154 rounded to the nearest hundred is 200. makes each statement true. Use each digit only once. B 1 Round 236 to the nearest ten. 1 2 3 4 5 6 7 8 9 Which tens is 236 between? Possible answer shown. -
21. Orthonormal Bases
21. Orthonormal Bases The canonical/standard basis 011 001 001 B C B C B C B0C B1C B0C e1 = B.C ; e2 = B.C ; : : : ; en = B.C B.C B.C B.C @.A @.A @.A 0 0 1 has many useful properties. • Each of the standard basis vectors has unit length: q p T jjeijj = ei ei = ei ei = 1: • The standard basis vectors are orthogonal (in other words, at right angles or perpendicular). T ei ej = ei ej = 0 when i 6= j This is summarized by ( 1 i = j eT e = δ = ; i j ij 0 i 6= j where δij is the Kronecker delta. Notice that the Kronecker delta gives the entries of the identity matrix. Given column vectors v and w, we have seen that the dot product v w is the same as the matrix multiplication vT w. This is the inner product on n T R . We can also form the outer product vw , which gives a square matrix. 1 The outer product on the standard basis vectors is interesting. Set T Π1 = e1e1 011 B C B0C = B.C 1 0 ::: 0 B.C @.A 0 01 0 ::: 01 B C B0 0 ::: 0C = B. .C B. .C @. .A 0 0 ::: 0 . T Πn = enen 001 B C B0C = B.C 0 0 ::: 1 B.C @.A 1 00 0 ::: 01 B C B0 0 ::: 0C = B. .C B. .C @. .A 0 0 ::: 1 In short, Πi is the diagonal square matrix with a 1 in the ith diagonal position and zeros everywhere else. -
Sabermetrics: the Past, the Present, and the Future
Sabermetrics: The Past, the Present, and the Future Jim Albert February 12, 2010 Abstract This article provides an overview of sabermetrics, the science of learn- ing about baseball through objective evidence. Statistics and baseball have always had a strong kinship, as many famous players are known by their famous statistical accomplishments such as Joe Dimaggio’s 56-game hitting streak and Ted Williams’ .406 batting average in the 1941 baseball season. We give an overview of how one measures performance in batting, pitching, and fielding. In baseball, the traditional measures are batting av- erage, slugging percentage, and on-base percentage, but modern measures such as OPS (on-base percentage plus slugging percentage) are better in predicting the number of runs a team will score in a game. Pitching is a harder aspect of performance to measure, since traditional measures such as winning percentage and earned run average are confounded by the abilities of the pitcher teammates. Modern measures of pitching such as DIPS (defense independent pitching statistics) are helpful in isolating the contributions of a pitcher that do not involve his teammates. It is also challenging to measure the quality of a player’s fielding ability, since the standard measure of fielding, the fielding percentage, is not helpful in understanding the range of a player in moving towards a batted ball. New measures of fielding have been developed that are useful in measuring a player’s fielding range. Major League Baseball is measuring the game in new ways, and sabermetrics is using this new data to find better mea- sures of player performance. -
Molecular Symmetry
Molecular Symmetry Symmetry helps us understand molecular structure, some chemical properties, and characteristics of physical properties (spectroscopy) – used with group theory to predict vibrational spectra for the identification of molecular shape, and as a tool for understanding electronic structure and bonding. Symmetrical : implies the species possesses a number of indistinguishable configurations. 1 Group Theory : mathematical treatment of symmetry. symmetry operation – an operation performed on an object which leaves it in a configuration that is indistinguishable from, and superimposable on, the original configuration. symmetry elements – the points, lines, or planes to which a symmetry operation is carried out. Element Operation Symbol Identity Identity E Symmetry plane Reflection in the plane σ Inversion center Inversion of a point x,y,z to -x,-y,-z i Proper axis Rotation by (360/n)° Cn 1. Rotation by (360/n)° Improper axis S 2. Reflection in plane perpendicular to rotation axis n Proper axes of rotation (C n) Rotation with respect to a line (axis of rotation). •Cn is a rotation of (360/n)°. •C2 = 180° rotation, C 3 = 120° rotation, C 4 = 90° rotation, C 5 = 72° rotation, C 6 = 60° rotation… •Each rotation brings you to an indistinguishable state from the original. However, rotation by 90° about the same axis does not give back the identical molecule. XeF 4 is square planar. Therefore H 2O does NOT possess It has four different C 2 axes. a C 4 symmetry axis. A C 4 axis out of the page is called the principle axis because it has the largest n . By convention, the principle axis is in the z-direction 2 3 Reflection through a planes of symmetry (mirror plane) If reflection of all parts of a molecule through a plane produced an indistinguishable configuration, the symmetry element is called a mirror plane or plane of symmetry . -
Lecture 4: April 8, 2021 1 Orthogonality and Orthonormality
Mathematical Toolkit Spring 2021 Lecture 4: April 8, 2021 Lecturer: Avrim Blum (notes based on notes from Madhur Tulsiani) 1 Orthogonality and orthonormality Definition 1.1 Two vectors u, v in an inner product space are said to be orthogonal if hu, vi = 0. A set of vectors S ⊆ V is said to consist of mutually orthogonal vectors if hu, vi = 0 for all u 6= v, u, v 2 S. A set of S ⊆ V is said to be orthonormal if hu, vi = 0 for all u 6= v, u, v 2 S and kuk = 1 for all u 2 S. Proposition 1.2 A set S ⊆ V n f0V g consisting of mutually orthogonal vectors is linearly inde- pendent. Proposition 1.3 (Gram-Schmidt orthogonalization) Given a finite set fv1,..., vng of linearly independent vectors, there exists a set of orthonormal vectors fw1,..., wng such that Span (fw1,..., wng) = Span (fv1,..., vng) . Proof: By induction. The case with one vector is trivial. Given the statement for k vectors and orthonormal fw1,..., wkg such that Span (fw1,..., wkg) = Span (fv1,..., vkg) , define k u + u = v − hw , v i · w and w = k 1 . k+1 k+1 ∑ i k+1 i k+1 k k i=1 uk+1 We can now check that the set fw1,..., wk+1g satisfies the required conditions. Unit length is clear, so let’s check orthogonality: k uk+1, wj = vk+1, wj − ∑ hwi, vk+1i · wi, wj = vk+1, wj − wj, vk+1 = 0. i=1 Corollary 1.4 Every finite dimensional inner product space has an orthonormal basis. -
Orthonormality and the Gram-Schmidt Process
Unit 4, Section 2: The Gram-Schmidt Process Orthonormality and the Gram-Schmidt Process The basis (e1; e2; : : : ; en) n n for R (or C ) is considered the standard basis for the space because of its geometric properties under the standard inner product: 1. jjeijj = 1 for all i, and 2. ei, ej are orthogonal whenever i 6= j. With this idea in mind, we record the following definitions: Definitions 6.23/6.25. Let V be an inner product space. • A list of vectors in V is called orthonormal if each vector in the list has norm 1, and if each pair of distinct vectors is orthogonal. • A basis for V is called an orthonormal basis if the basis is an orthonormal list. Remark. If a list (v1; : : : ; vn) is orthonormal, then ( 0 if i 6= j hvi; vji = 1 if i = j: Example. The list (e1; e2; : : : ; en) n n forms an orthonormal basis for R =C under the standard inner products on those spaces. 2 Example. The standard basis for Mn(C) consists of n matrices eij, 1 ≤ i; j ≤ n, where eij is the n × n matrix with a 1 in the ij entry and 0s elsewhere. Under the standard inner product on Mn(C) this is an orthonormal basis for Mn(C): 1. heij; eiji: ∗ heij; eiji = tr (eijeij) = tr (ejieij) = tr (ejj) = 1: 1 Unit 4, Section 2: The Gram-Schmidt Process 2. heij; ekli, k 6= i or j 6= l: ∗ heij; ekli = tr (ekleij) = tr (elkeij) = tr (0) if k 6= i, or tr (elj) if k = i but l 6= j = 0: So every vector in the list has norm 1, and every distinct pair of vectors is orthogonal. -
Call Numbers
Call numbers: It is our recommendation that libraries NOT put J, +, E, Ref, etc. in the call number field in front of the Dewey or other call number. Use the Home Location field to indicate the collection for the item. It is difficult if not impossible to sort lists if the call number fields aren’t entered systematically. Dewey Call Numbers for Non-Fiction Each library follows its own practice for how long a Dewey number they use and what letters are used for the author’s name. Some libraries use a number (Cutter number from a table) after the letters for the author’s name. Other just use letters for the author’s name. Call Numbers for Fiction For fiction, the call number is usually the author’s Last Name, First Name. (Use a comma between last and first name.) It is usually already in the call number field when you barcode. Call Numbers for Paperbacks Each library follows its own practice. Just be consistent for easier handling of the weeding lists. WCTS libraries should follow the format used by WCTS for the items processed by them for your library. Most call numbers are either the author’s name or just the first letters of the author’s last name. Please DO catalog your paperbacks so they can be shared with other libraries. Call Numbers for Magazines To get the call numbers to display in the correct order by date, the call number needs to begin with the date of the issue in a number format, followed by the issue in alphanumeric format. -
Minorities and Women in Television See Little Change, While Minorities Fare Worse in Radio
RunningRunning inin PlacePlace Minorities and women in television see little change, while minorities fare worse in radio. By Bob Papper he latest figures from the RTNDA/Ball State Uni- Minority Population vs. Minority Broadcast Workforce versity Annual Survey show lit- 2005 2004 2000 1995 1990 tle change for minorities in tel- evision news in the past year but Minority Population in U.S. 33.2% 32.8% 30.9% 27.9% 25.9% slippage in radio news. Minority TV Workforce 21.2 21.8 21.0 17.1 17.8 TIn television, the overall minority Minority Radio Workforce 7.9 11.8 10.0 14.7 10.8 workforce remained largely un- Source for U.S. numbers: U.S. Census Bureau changed at 21.2 percent, compared with last year’s 21.8 percent. At non-Hispanic stations, the the stringent Equal Employment minority workforce in TV news is up minority workforce also remained Opportunity rules were eliminated in 3.4 percent. At the same time, the largely steady at 19.5 percent, com- 1998. minority population in the U.S. has pared with 19.8 percent a year ago. News director numbers were increased 7.3 percent. Overall, the After a jump in last year’s minority mixed, with the percentage of minor- minority workforce in TV has been at radio numbers, the percentage fell this ity TV news directors down slightly to 20 percent—plus or minus 3 per- year.The minority radio news work- 12 percent (from 12.5 percent last cent—for every year in the past 15. -
Precise Radioactivity Measurements a Controversy
http://cyclotron.tamu.edu Precise Radioactivity Measurements: A Controversy Settled Simultaneous measurements of x-rays and gamma rays emitted in radioactive nuclear decays probe how frequently excited nuclei release energy by ejecting an atomic electron THE SCIENCE Radioactivity takes several different forms. One is when atomic nuclei in an excited state release their excess energy (i.e., they decay) by emitting a type of electromagnetic radiation, called gamma rays. Sometimes, rather than a gamma ray being emitted, the nucleus conveys its energy electromagnetically to an atomic electron, causing it to be ejected at high speed instead. The latter process is called internal conversion and, for a particular radioactive decay, the probability of electron emission relative to that of gamma-ray emission is called the internal conversion coefficient (ICC). Theoretically, for almost all transitions, the ICC is expected to depend on the quantum numbers of the participating nuclear excited states and on the amount of energy released, but not on the sometimes obscure details of how the nucleus is structured. For the first time, scientists have been able to test the theory to percent precision, verifying its independence from nuclear structure. At the same time, the new results have guided theorists to make improvements in their ICC calculations. THE IMPACT For the decays of most known excited states in nuclei, only the gamma rays have been observed, so scientists have had to combine measured gamma-ray intensities with calculated ICCs in order to put together a complete picture known as a decay scheme, which includes the contribution of electron as well as gamma-ray emission, for every radioactive decay. -
Girls' Elite 2 0 2 0 - 2 1 S E a S O N by the Numbers
GIRLS' ELITE 2 0 2 0 - 2 1 S E A S O N BY THE NUMBERS COMPARING NORMAL SEASON TO 2020-21 NORMAL 2020-21 SEASON SEASON SEASON LENGTH SEASON LENGTH 6.5 Months; Dec - Jun 6.5 Months, Split Season The 2020-21 Season will be split into two segments running from mid-September through mid-February, taking a break for the IHSA season, and then returning May through mid- June. The season length is virtually the exact same amount of time as previous years. TRAINING PROGRAM TRAINING PROGRAM 25 Weeks; 157 Hours 25 Weeks; 156 Hours The training hours for the 2020-21 season are nearly exact to last season's plan. The training hours do not include 16 additional in-house scrimmage hours on the weekends Sep-Dec. Courtney DeBolt-Slinko returns as our Technical Director. 4 new courts this season. STRENGTH PROGRAM STRENGTH PROGRAM 3 Days/Week; 72 Hours 3 Days/Week; 76 Hours Similar to the Training Time, the 2020-21 schedule will actually allow for a 4 additional hours at Oak Strength in our Sparta Science Strength & Conditioning program. These hours are in addition to the volleyball-specific Training Time. Oak Strength is expanding by 8,800 sq. ft. RECRUITING SUPPORT RECRUITING SUPPORT Full Season Enhanced Full Season In response to the recruiting challenges created by the pandemic, we are ADDING livestreaming/recording of scrimmages and scheduled in-person visits from Lauren, Mikaela or Peter. This is in addition to our normal support services throughout the season. TOURNAMENT DATES TOURNAMENT DATES 24-28 Dates; 10-12 Events TBD Dates; TBD Events We are preparing for 15 Dates/6 Events Dec-Feb. -
Symmetry Numbers and Chemical Reaction Rates
Theor Chem Account (2007) 118:813–826 DOI 10.1007/s00214-007-0328-0 REGULAR ARTICLE Symmetry numbers and chemical reaction rates Antonio Fernández-Ramos · Benjamin A. Ellingson · Rubén Meana-Pañeda · Jorge M. C. Marques · Donald G. Truhlar Received: 14 February 2007 / Accepted: 25 April 2007 / Published online: 11 July 2007 © Springer-Verlag 2007 Abstract This article shows how to evaluate rotational 1 Introduction symmetry numbers for different molecular configurations and how to apply them to transition state theory. In general, Transition state theory (TST) [1–6] is the most widely used the symmetry number is given by the ratio of the reactant and method for calculating rate constants of chemical reactions. transition state rotational symmetry numbers. However, spe- The conventional TST rate expression may be written cial care is advised in the evaluation of symmetry numbers kBT QTS(T ) in the following situations: (i) if the reaction is symmetric, k (T ) = σ exp −V ‡/k T (1) TST h (T ) B (ii) if reactants and/or transition states are chiral, (iii) if the R reaction has multiple conformers for reactants and/or tran- where kB is Boltzmann’s constant; h is Planck’s constant; sition states and, (iv) if there is an internal rotation of part V ‡ is the classical barrier height; T is the temperature and σ of the molecular system. All these four situations are treated is the reaction-path symmetry number; QTS(T ) and R(T ) systematically and analyzed in detail in the present article. are the quantum mechanical transition state quasi-partition We also include a large number of examples to clarify some function and reactant partition function, respectively, without complicated situations, and in the last section we discuss an rotational symmetry numbers, and with the zeroes of energy example involving an achiral diasteroisomer.